Multiply the following complex numbers: $({-1-4i}) \cdot ({2+i})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-1-4i}) \cdot ({2+i}) = $ $ ({-1} \cdot {2}) + ({-1} \cdot {1}i) + ({-4}i \cdot {2}) + ({-4}i \cdot {1}i) $ Then simplify the terms: $ (-2) + (-1i) + (-8i) + (-4 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -2 + (-1 - 8)i - 4i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -2 + (-1 - 8)i - (-4) $ The result is simplified: $ (-2 + 4) + (-9i) = 2-9i $